Comte's central claim is a developmental one. Every branch of human knowledge, he held, passes through three stages. In the theological stage, events are explained by the will of personal beings, spirits or gods. In the metaphysical stage, the gods are replaced by abstractions, essences and forces, which he regarded as gods with the personality drained out. In the positive stage, the search for ultimate causes is abandoned altogether and enquiry confines itself to the laws that relate observable phenomena to one another.
The sciences reach that third stage at different times, in an order fixed by how complex and how close to human concerns their subject is: mathematics first, then astronomy, physics, chemistry, biology, and last of all the study of society. That final science had no name, so he supplied one, coining sociologie in the fourth volume of the Cours de philosophie positive. He coined altruisme too, and the pairing matters: the new science was to supply the knowledge on which a reorganised society would rest, and the new morality was to supply its motive.
The scheme has not worn well as history, since the stages do not appear in that order in any actual society and theology has not obliged by disappearing. It has worn extremely well as a founding statement, and the discipline that got its name from him has never quite stopped arguing with the account of itself he gave it.